P-release kinetic as a predictor for P-availability in the STYCS Trials
In my Internship I studied the current GRUD, particularly Mg, P and K
Fertilizer requirement models imply \(Y\sim STP + Clay\) & \(P-\text{Export}\sim STP + Clay\)
Currently only stationary measurement of STP are considered
Could a kinetic desorption-model better explain the soil status and yield data?
The net-desorption was modeled using a first-order kinetic equation:
1. The Rate of Release: The change in P over time is proportional to the remaining desorbable P. \[\frac{dP}{dt}=k \times (P^S-P)\]
2. The Solution: When solved, this gives us the equation for the curve: \[P(t)=P^S \times (1-e^{-kt})\]
We compared two approaches to predict agronomic outcomes:
The Standard Method
These are static “snapshots” of the soil’s P capacity.
The Kinetic Method
This approach measures P as a dynamic process.
We tested the models against three agronomic metrics:
1. Normalized Yield (\(Y_{norm}\)) - How well did the crop perform relative to its maximum potential at that specific site?
2. P-Export (\(P_{up}\)) - How much phosphorus did the crop remove from the field?
3. P-Balance (\(P_{bal}\)) - What is the long-term surplus or deficit of P in the soil? This is a key indicator of sustainability.
To ensure a fair and robust comparison, we used a consistent statistical approach:
1. Linear Mixed-Effects Models (lmer) - We built a separate model for each agronomic outcome (Yield, P-Export, P-Balance). - This approach accounts for the nested structure of the STYCS experiment (sites, years, blocks).
2. Standardized Coefficients (β) - All numeric variables were scaled and centered (mean=0, sd=1). - This allows us to directly compare the effect size of each predictor. A larger coefficient means a stronger effect.
3. The Comparison - In the following tables, each column represents a separate model where we test a different set of predictors.
A robust P metric should reflect both the soil’s inherent properties (like texture and pH) and the impact of management (fertilization). We modeled each metric to see what drives it.
| Model | $PS$ | $k$ | $J_0$ | $P_{CO_2}$ | $P_{AAE10}$ |
|---|---|---|---|---|---|
| Alox | 0.136 | -0.660 | -1.204 | -0.034 | -0.319 |
| Feox | -0.098 | 0.020 | -0.571 | -0.164 | -0.138 |
| Clay | -0.062 | -1.733** | 0.611 | -0.007 | -0.121 |
| $C_{org}$ | 0.351* | 1.044** | -0.412 | 0.166 | 0.232 |
| pH | -0.058 | -0.280 | 0.094 | 0.075 | 0.057 |
| Silt | -0.046 | 0.252 | 0.113 | -0.084 | 0.012 |
| $R^2_m$ | 0.175 | 0.204 | 0.224 | 0.125 | 0.280 |
| $R^2_c$ | 0.894 | 0.963 | 0.976 | 0.724 | 0.832 |
The following random structure was chosen:
(1|year) + (1|Site) + (1|Site:block) + (Treatment|Site)
| Model | m.PS | m.k | m.log(k*PS) | m.PCO2 | m.PAAE10 |
|---|---|---|---|---|---|
| (Intercept) | -0.848* | -0.425 | 0.039 | -0.536 | -0.532 |
| Alox | 0.136 | -0.660 | -1.204 | -0.034 | -0.319 |
| Feox | -0.098 | 0.020 | -0.571 | -0.164 | -0.138 |
| soil_0_20_clay | -0.062 | -1.733** | 0.611 | -0.007 | -0.121 |
| soil_0_20_Corg | 0.351* | 1.044** | -0.412 | 0.166 | 0.232 |
| soil_0_20_pH_H2O | -0.058 | -0.280 | 0.094 | 0.075 | 0.057 |
| soil_0_20_silt | -0.046 | 0.252 | 0.113 | -0.084 | 0.012 |
| R2m | 0.175 | 0.204 | 0.224 | 0.125 | 0.280 |
| R2c | 0.894 | 0.963 | 0.976 | 0.724 | 0.832 |
Observation
| Model | Yn-STP-CO2 | Yn-STP-AAE10 | Yn-STP-GRUD | Yn-Kinetic |
|---|---|---|---|---|
| (Intercept) | 0.012 | 0.007 | -0.109 | 0.156 |
| k | 0.166 | |||
| k:log(PS) | -0.012 | |||
| log(PS) | 0.066 | |||
| log(soil_0_20_P_AAE10) | 0.067* | 0.432** | ||
| log(soil_0_20_P_CO2) | 0.027 | -0.128 | ||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.149* | |||
| R2m | 0.012 | 0.084 | 0.291 | 0.019 |
| R2c | 0.083 | 0.361 | 0.436 | 0.045 |
Observation
| Model | CO2_Pexport | AAE10_Pexport | Grud_Pexport | Kin_Pexport |
|---|---|---|---|---|
| (Intercept) | 0.012 | -0.002 | 0.119 | 0.596 |
| k | -0.014 | |||
| k:log(PS) | 0.080 | |||
| log(PS) | -0.018 | |||
| log(soil_0_20_P_AAE10) | 0.025 | -0.015 | ||
| log(soil_0_20_P_CO2) | 0.087 | 0.131 | ||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.011 | |||
| R2m | 0.012 | 0.001 | 0.016 | 0.004 |
| R2c | 0.654 | 0.685 | 0.796 | 0.789 |
Observations
| Model | CO2_Pbalance | AAE10_Pbalance | Grud_Pbalance | Kin_Pbalance |
|---|---|---|---|---|
| (Intercept) | 0.569* | 0.315 | 0.610* | 1.086* |
| k | 0.155 | |||
| k:log(PS) | -0.151 | |||
| log(PS) | 0.341*** | |||
| log(soil_0_20_P_AAE10) | 0.009 | 0.009 | ||
| log(soil_0_20_P_CO2) | -0.023 | -0.029 | ||
| log(soil_0_20_P_CO2):log(soil_0_20_P_AAE10) | 0.030 | |||
| R2m | 0.001 | 0.000 | 0.006 | 0.122 |
| R2c | 0.590 | 0.762 | 0.596 | 0.699 |
Observation
Thank you for your attention